Question: Simplify the following expression: $ n = \dfrac{1}{9} + \dfrac{r + 4}{7r - 9} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7r - 9}{7r - 9}$ $ \dfrac{1}{9} \times \dfrac{7r - 9}{7r - 9} = \dfrac{7r - 9}{63r - 81} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{r + 4}{7r - 9} \times \dfrac{9}{9} = \dfrac{9r + 36}{63r - 81} $ Therefore $ n = \dfrac{7r - 9}{63r - 81} + \dfrac{9r + 36}{63r - 81} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{7r - 9 + 9r + 36}{63r - 81} $ $n = \dfrac{16r + 27}{63r - 81}$